Error mitigation with Clifford quantum-circuit data
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
| Published: | 2021-11-26, volume 5, page 592 |
| Eprint: | arXiv:2005.10189v3 |
| Doi: | https://doi.org/10.22331/q-2021-11-26-592 |
| Citation: | Quantum 5, 592 (2021). |
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Abstract
Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data $\{X_i^{\text{noisy}},X_i^{\text{exact}}\}$ via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where $X_i^{\text{noisy}}$ and $X_i^{\text{exact}}$ are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.
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► References
[1] Scott Aaronson and Daniel Gottesman. Improved simulation of stabilizer circuits. Phys. Rev. A, 70: 052328, Nov 2004. 10.1103/PhysRevA.70.052328.
https://doi.org/10.1103/PhysRevA.70.052328
[2] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. Quantum supremacy using a programmable superconducting processor. Nature, 574 (7779): 505–510, 2019. https://doi.org/10.5061/dryad.k6t1rj8.
https://doi.org/10.5061/dryad.k6t1rj8
[3] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alán Aspuru-Guzik. Noisy intermediate-scale quantum (nisq) algorithms. arXiv preprint arXiv:2101.08448, 2021. URL https://arxiv.org/abs/2101.08448.
arXiv:2101.08448
[4] Xavi Bonet-Monroig, Ramiro Sagastizabal, M Singh, and TE O'Brien. Low-cost error mitigation by symmetry verification. Physical Review A, 98 (6): 062339, 2018. 10.1103/PhysRevA.98.062339.
https://doi.org/10.1103/PhysRevA.98.062339
[5] Sergey Bravyi, Sarah Sheldon, Abhinav Kandala, David C. Mckay, and Jay M. Gambetta. Mitigating measurement errors in multiqubit experiments. Phys. Rev. A, 103: 042605, Apr 2021. 10.1103/PhysRevA.103.042605.
https://doi.org/10.1103/PhysRevA.103.042605
[6] Zhenyu Cai. Multi-exponential error extrapolation and combining error mitigation techniques for nisq applications. npj Quantum Information, 7 (1): 80, May 2021a. ISSN 2056-6387. 10.1038/s41534-021-00404-3.
https://doi.org/10.1038/s41534-021-00404-3
[7] Zhenyu Cai. Quantum error mitigation using symmetry expansion. arXiv preprint arXiv:2101.03151, 2021b. URL https://arxiv.org/abs/2101.03151. 10.22331/q-2021-09-21-548.
https://doi.org/10.22331/q-2021-09-21-548
arXiv:2101.03151
[8] Yudong Cao, Jonathan Romero, Jonathan P Olson, Matthias Degroote, Peter D Johnson, Mária Kieferová, Ian D Kivlichan, Tim Menke, Borja Peropadre, Nicolas PD Sawaya, et al. Quantum chemistry in the age of quantum computing. Chemical reviews, 119 (19): 10856–10915, 2019. 10.1021/acs.chemrev.8b00803.
https://doi.org/10.1021/acs.chemrev.8b00803
[9] M Cerezo, Kunal Sharma, Andrew Arrasmith, and Patrick J Coles. Variational quantum state eigensolver. arXiv preprint arXiv:2004.01372, 2020. URL https://arxiv.org/abs/2004.01372.
arXiv:2004.01372
[10] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles. Variational quantum algorithms. Nature Reviews Physics, 3 (9): 625–644, Sep 2021. ISSN 2522-5820. 10.1038/s42254-021-00348-9.
https://doi.org/10.1038/s42254-021-00348-9
[11] J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, Lev S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Detecting highly entangled states with a joint qubit readout. Phys. Rev. A, 81: 062325, Jun 2010. 10.1103/PhysRevA.81.062325.
https://doi.org/10.1103/PhysRevA.81.062325
[12] L. Cincio, Y. Subaşı, A. T. Sornborger, and P. J. Coles. Learning the quantum algorithm for state overlap. New Journal of Physics, 20 (11): 113022, 2018. 10.1088/1367-2630/aae94a.
https://doi.org/10.1088/1367-2630/aae94a
[13] Lukasz Cincio, Kenneth Rudinger, Mohan Sarovar, and Patrick J. Coles. Machine learning of noise-resilient quantum circuits. PRX Quantum, 2: 010324, Feb 2021. 10.1103/PRXQuantum.2.010324.
https://doi.org/10.1103/PRXQuantum.2.010324
[14] G. E. Crooks. Performance of the quantum approximate optimization algorithm on the maximum cut problem. arXiv preprint arXiv:1811.08419, 2018. URL https://arxiv.org/abs/1811.0841. 10.1126/sciadv.aaz0418.
https://doi.org/10.1126/sciadv.aaz0418
arXiv:1811.08419
https://arxiv.org/abs/1811.0841
[15] Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, and Jay M. Gambetta. Validating quantum computers using randomized model circuits. Phys. Rev. A, 100: 032328, Sep 2019. 10.1103/PhysRevA.100.032328.
https://doi.org/10.1103/PhysRevA.100.032328
[16] Eugene F Dumitrescu, Alex J McCaskey, Gaute Hagen, Gustav R Jansen, Titus D Morris, T Papenbrock, Raphael C Pooser, David Jarvis Dean, and Pavel Lougovski. Cloud quantum computing of an atomic nucleus. Physical review letters, 120 (21): 210501, 2018. 10.1103/PhysRevLett.120.210501.
https://doi.org/10.1103/PhysRevLett.120.210501
[17] Suguru Endo, Simon C. Benjamin, and Ying Li. Practical quantum error mitigation for near-future applications. Phys. Rev. X, 8: 031027, Jul 2018. 10.1103/PhysRevX.8.031027.
https://doi.org/10.1103/PhysRevX.8.031027
[18] Suguru Endo, Zhenyu Cai, Simon C Benjamin, and Xiao Yuan. Hybrid quantum-classical algorithms and quantum error mitigation. Journal of the Physical Society of Japan, 90 (3): 032001, 2021. 10.7566/JPSJ.90.032001.
https://doi.org/10.7566/JPSJ.90.032001
[19] Héctor Abraham et. al. Qiskit: An open-source framework for quantum computing, 2019. URL https://zenodo.org/record/2562111. 10.5281/zenodo.2562111.
https://doi.org/10.5281/zenodo.2562111
https://zenodo.org/record/2562111
[20] M. Fannes, B. Nachtergaele, and R. F. Werner. Finitely correlated states on quantum spin chains. Communications in Mathematical Physics, 144 (3): 443–490, Mar 1992. ISSN 1432-0916. 10.1007/BF02099178.
https://doi.org/10.1007/BF02099178
[21] E. Farhi, J. Goldstone, and S. Gutmann. A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, 2014. URL https://arxiv.org/abs/1411.4028.
arXiv:1411.4028
[22] Andrew J. Ferris and Guifre Vidal. Perfect sampling with unitary tensor networks. Phys. Rev. B, 85: 165146, Apr 2012. 10.1103/PhysRevB.85.165146.
https://doi.org/10.1103/PhysRevB.85.165146
[23] Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, Andrea Mari, and William J. Zeng. Digital zero noise extrapolation for quantum error mitigation. pages 306–316, Oct 2020. 10.1109/QCE49297.2020.00045.
https://doi.org/10.1109/QCE49297.2020.00045
[24] Daniel Gottesman. An introduction to quantum error correction and fault-tolerant quantum computation. arXiv preprint arXiv:0904.2557, 2009. URL https://arxiv.org/abs/0904.2557.
arXiv:0904.2557
[25] Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor G. Rieffel, Davide Venturelli, and Rupak Biswas. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms, 12 (2), 2019. ISSN 1999-4893. 10.3390/a12020034.
https://doi.org/10.3390/a12020034
[26] Andre He, Benjamin Nachman, Wibe A. de Jong, and Christian W. Bauer. Zero-noise extrapolation for quantum-gate error mitigation with identity insertions. Phys. Rev. A, 102: 012426, Jul 2020. 10.1103/PhysRevA.102.012426.
https://doi.org/10.1103/PhysRevA.102.012426
[27] Abhijith J., Adetokunbo Adedoyin, John Ambrosiano, Petr Anisimov, Andreas Bärtschi, William Casper, Gopinath Chennupati, Carleton Coffrin, Hristo Djidjev, David Gunter, Satish Karra, Nathan Lemons, Shizeng Lin, Alexander Malyzhenkov, David Mascarenas, Susan Mniszewski, Balu Nadiga, Daniel O'Malley, Diane Oyen, Scott Pakin, Lakshman Prasad, Randy Roberts, Phillip Romero, Nandakishore Santhi, Nikolai Sinitsyn, Pieter J. Swart, James G. Wendelberger, Boram Yoon, Richard Zamora, Wei Zhu, Stephan Eidenbenz, Patrick J. Coles, Marc Vuffray, and Andrey Y. Lokhov. Quantum algorithm implementations for beginners, 2018. URL https://arxiv.org/abs/1804.03719.
arXiv:1804.03719
[28] Abhinav Kandala, Kristan Temme, Antonio D Córcoles, Antonio Mezzacapo, Jerry M Chow, and Jay M Gambetta. Error mitigation extends the computational reach of a noisy quantum processor. Nature, 567 (7749): 491–495, 2019. 10.1038/s41586-019-1040-7.
https://doi.org/10.1038/s41586-019-1040-7
[29] S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles. Quantum-assisted quantum compiling. Quantum, 3: 140, May 2019. ISSN 2521-327X. 10.22331/q-2019-05-13-140.
https://doi.org/10.22331/q-2019-05-13-140
[30] Ryan LaRose, Arkin Tikku, Étude O'Neel-Judy, Lukasz Cincio, and Patrick J. Coles. Variational quantum state diagonalization. npj Quantum Information, 5 (1): 57, Jun 2019. ISSN 2056-6387. 10.1038/s41534-019-0167-6.
https://doi.org/10.1038/s41534-019-0167-6
[31] Y. Li and S. C. Benjamin. Efficient variational quantum simulator incorporating active error minimization. Phys. Rev. X, 7: 021050, Jun 2017. 10.1103/PhysRevX.7.021050.
https://doi.org/10.1103/PhysRevX.7.021050
[32] Sam McArdle, Xiao Yuan, and Simon Benjamin. Error-mitigated digital quantum simulation. Phys. Rev. Lett., 122: 180501, May 2019. 10.1103/PhysRevLett.122.180501.
https://doi.org/10.1103/PhysRevLett.122.180501
[33] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan. Quantum computational chemistry. Reviews of Modern Physics, 92 (1): 015003, 2020. https://doi.org/10.1103/RevModPhys.92.015003.
https://doi.org/10.1103/RevModPhys.92.015003
[34] Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. 18 (2): 023023, feb 2016. 10.1088/1367-2630/18/2/023023.
https://doi.org/10.1088/1367-2630/18/2/023023
[35] Prakash Murali, Jonathan M Baker, Ali Javadi-Abhari, Frederic T Chong, and Margaret Martonosi. Noise-adaptive compiler mappings for noisy intermediate-scale quantum computers. In Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, pages 1015–1029, 2019. https://doi.org/10.1145/3297858.3304075.
https://doi.org/10.1145/3297858.3304075
[36] Michael A Nielsen. Neural networks and deep learning, volume 2018. Determination press San Francisco, CA, USA:, 2015.
[37] Matthew Otten and Stephen K Gray. Recovering noise-free quantum observables. Physical Review A, 99 (1): 012338, 2019. 10.1103/PhysRevA.99.012338.
https://doi.org/10.1103/PhysRevA.99.012338
[38] Matthew Otten, Cristian L Cortes, and Stephen K Gray. Noise-resilient quantum dynamics using symmetry-preserving ansatzes. arXiv preprint arXiv:1910.06284, 2019. URL https://arxiv.org/abs/1910.06284.
arXiv:1910.06284
[39] Hakop Pashayan, Oliver Reardon-Smith, Kamil Korzekwa, and Stephen D. Bartlett. Fast estimation of outcome probabilities for quantum circuits. arXiv:2101.12223, 2021. URL https://arxiv.org/abs/2101.12223.
arXiv:2101.12223
[40] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien. A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5: 4213, 2014. 10.1038/ncomms5213.
https://doi.org/10.1038/ncomms5213
[41] John Preskill. Quantum computing in the NISQ era and beyond. Quantum, 2: 79, 2018. 10.22331/q-2018-08-06-79.
https://doi.org/10.22331/q-2018-08-06-79
[42] Kunal Sharma, Sumeet Khatri, M Cerezo, and Patrick J Coles. Noise resilience of variational quantum compiling. 22 (4): 043006, apr 2020. 10.1088/1367-2630/ab784c.
https://doi.org/10.1088/1367-2630/ab784c
[43] Rolando D Somma. Quantum eigenvalue estimation via time series analysis. New Journal of Physics, 21 (12): 123025, 2019. https://doi.org/10.1088/1367-2630/ab5c60.
https://doi.org/10.1088/1367-2630/ab5c60
[44] Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C. Benjamin, and Ying Li. Learning-based quantum error mitigation. PRX Quantum, 2: 040330, Nov 2021. 10.1103/PRXQuantum.2.040330.
https://doi.org/10.1103/PRXQuantum.2.040330
[45] Kristan Temme, Sergey Bravyi, and Jay M Gambetta. Error mitigation for short-depth quantum circuits. Physical review letters, 119 (18): 180509, 2017. 10.1103/PhysRevLett.119.180509.
https://doi.org/10.1103/PhysRevLett.119.180509
[46] Giacomo Torlai, Guglielmo Mazzola, Giuseppe Carleo, and Antonio Mezzacapo. Precise measurement of quantum observables with neural-network estimators. Phys. Rev. Research, 2: 022060, Jun 2020. 10.1103/PhysRevResearch.2.022060.
https://doi.org/10.1103/PhysRevResearch.2.022060
[47] Don Van Ravenzwaaij, Pete Cassey, and Scott D Brown. A simple introduction to markov chain monte–carlo sampling. Psychonomic bulletin & review, 25 (1): 143–154, 2018. 10.3758/s13423-016-1015-8.
https://doi.org/10.3758/s13423-016-1015-8
[48] Xiao Yuan, Suguru Endo, Qi Zhao, Ying Li, and Simon C Benjamin. Theory of variational quantum simulation. Quantum, 3: 191, 2019. https://doi.org/10.22331/q-2019-10-07-191.
https://doi.org/10.22331/q-2019-10-07-191
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[6] Hrushikesh Pramod Patil, Peiyi Li, Ji Liu, and Huiyang Zhou, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 898 (2023) ISBN:979-8-3503-4323-6.
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[8] Jordi Pérez-Guijarro, Alba Pagès-Zamora, and Javier R. Fonollosa, ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 9691 (2024) ISBN:979-8-3503-4485-1.
[9] Julius Mildenberger, Wojciech Mruczkiewicz, Jad C. Halimeh, Zhang Jiang, and Philipp Hauke, "Confinement in a $${{\mathbb{Z}}}_{2}$$ lattice gauge theory on a quantum computer", Nature Physics 21 2, 312 (2025).
[10] Noah F. Berthusen, Thaís V. Trevisan, Thomas Iadecola, and Peter P. Orth, "Quantum dynamics simulations beyond the coherence time on noisy intermediate-scale quantum hardware by variational Trotter compression", Physical Review Research 4 2, 023097 (2022).
[11] Ali Shaib, Mohamad Hussein Naim, Mohammed E. Fouda, Rouwaida Kanj, and Fadi Kurdahi, "Efficient noise mitigation technique for quantum computing", Scientific Reports 13 1, 3912 (2023).
[12] Tim Weaving, Alexis Ralli, Peter J. Love, Sauro Succi, and Peter V. Coveney, "Accurately Simulating the Time Evolution of an Ising Model with Echo Verified Clifford Data Regression on a Superconducting Quantum Computer", Quantum 9, 1732 (2025).
[13] Qingxin Yang and Stefano Markidis, Proceedings of the 40th ACM International Conference on Supercomputing - Workshops 125 (2026) ISBN:9798400723001.
[14] Ning Ma, Proceedings of the 34th ACM International Conference on the Foundations of Software Engineering 25 (2026) ISBN:9798400726361.
[15] Phalgun Lolur, Mårten Skogh, Werner Dobrautz, Christopher Warren, Janka Biznárová, Amr Osman, Giovanna Tancredi, Göran Wendin, Jonas Bylander, and Martin Rahm, "Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry", Journal of Chemical Theory and Computation 19 3, 783 (2023).
[16] Oskar Graulund Lentz Rasmussen, Erik Kjellgren, Peter Reinholdt, Stephan P. A. Sauer, Sonia Coriani, Karl Michael Ziems, and Jacob Kongsted, "Cost-Effective Scalable Quantum Error Mitigation for Tiled Ansätze", Journal of Chemical Theory and Computation (2026).
[17] Róbert Trényi, Árpád Lukács, Paweł Horodecki, Ryszard Horodecki, Tamás Vértesi, and Géza Tóth, "Activation of metrologically useful genuine multipartite entanglement", New Journal of Physics 26 2, 023034 (2024).
[18] Thomas Ayral, Pauline Besserve, Denis Lacroix, and Edgar Andres Ruiz Guzman, "Quantum computing with and for many-body physics", The European Physical Journal A 59 10, 227 (2023).
[19] Vedika Saravanan and Samah Mohamed Saeed, Proceedings of the 41st IEEE/ACM International Conference on Computer-Aided Design 1 (2022) ISBN:9781450392174.
[20] Cheng-Yun Hsieh, Hsin-Ying Tsai, Yuan-Hsiang Lu, and James Chien-Mo Li, "Small Sampling Overhead Error Mitigation for Quantum Circuits", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 43 3, 826 (2024).
[21] Bo Yang, Rudy Raymond, and Shumpei Uno, "Efficient quantum readout-error mitigation for sparse measurement outcomes of near-term quantum devices", Physical Review A 106 1, 012423 (2022).
[22] L. Domingo, M. Djukic, C. Johnson, and F. Borondo, "Binding affinity predictions with hybrid quantum-classical convolutional neural networks", Scientific Reports 13 1, 17951 (2023).
[23] Shengxin Zhuang, John Tanner, Yusen Wu, Du Huynh, Wei Liu, Xavier Cadet, Nicolas Fontaine, Philippe Charton, Cedric Damour, Frederic Cadet, and Jingbo Wang, "Non-hemolytic peptide classification using a quantum support vector machine", Quantum Information Processing 23 11, 379 (2024).
[24] Roberto Ruiz, Alejandro Sopena, Balázs Pozsgay, and Esperanza López, "Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation", PRX Quantum 6 3, 030316 (2025).
[25] Lindsay Bassman Oftelie, Katherine Klymko, Diyi Liu, Norm M. Tubman, and Wibe A. de Jong, "Computing Free Energies with Fluctuation Relations on Quantum Computers", Physical Review Letters 129 13, 130603 (2022).
[26] Georgios Ioannou, Gopika Kizhuvettil, Mohammad Walid Charrwi, and Samah Mohamed Saeed, 2024 IEEE Computer Society Annual Symposium on VLSI (ISVLSI) 607 (2024) ISBN:979-8-3503-5411-9.
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[29] Wenbo Shi, Neel Kanth Kundu, and Robert Malaney, "Error-mitigated multi-layer quantum routing", APL Quantum 2 1, 016130 (2025).
[30] Keisuke Fujii, Kaoru Mizuta, Hiroshi Ueda, Kosuke Mitarai, Wataru Mizukami, and Yuya O. Nakagawa, "Deep Variational Quantum Eigensolver: A Divide-And-Conquer Method for Solving a Larger Problem with Smaller Size Quantum Computers", PRX Quantum 3 1, 010346 (2022).
[31] Gokul Subramanian Ravi, Pranav Gokhale, Yi Ding, William Kirby, Kaitlin Smith, Jonathan M. Baker, Peter J. Love, Henry Hoffmann, Kenneth R. Brown, and Frederic T. Chong, Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 1 15 (2022) ISBN:9781450399159.
[32] Friedrich Hübner, Eric Vernier, and Lorenzo Piroli, "Generalized hydrodynamics of integrable quantum circuits", SciPost Physics 18 4, 135 (2025).
[33] Tianyi Hao, Kun Liu, and Swamit Tannu, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.
[34] Yu Zhang, Lukasz Cincio, Christian F. A. Negre, Piotr Czarnik, Patrick J. Coles, Petr M. Anisimov, Susan M. Mniszewski, Sergei Tretiak, and Pavel A. Dub, "Variational quantum eigensolver with reduced circuit complexity", npj Quantum Information 8 1, 96 (2022).
[35] Yuta Shingu, Tetsuro Nikuni, Shiro Kawabata, and Yuichiro Matsuzaki, "Quantum annealing with error mitigation", Physical Review A 109 4, 042606 (2024).
[36] Saravanan K, Divakar G, Kaaviya K, Keerthivasan G, and Rahul K, 2025 IEEE 1st International Conference on Smart Innovations in Systems, Infrastructure, Mechanical, Power, AI and Computing Technologies (SISIMPACT) 1389 (2025) ISBN:979-8-3315-5787-4.
[37] Ken N. Okada, Keita Osaki, Kosuke Mitarai, and Keisuke Fujii, "Classically optimized variational quantum eigensolver with applications to topological phases", Physical Review Research 5 4, 043217 (2023).
[38] Bhuvanesh Sundar, Bram Evert, Vasily Geyko, Andrew Patterson, Ilon Joseph, and Yuan Shi, "Simulating plasma wave propagation on a superconducting quantum chip", Physical Review Applied 25 2, 024077 (2026).
[39] Siyuan Niu, Aida Todri-Sanial, and Nicholas T Bronn, "Multi-qubit dynamical decoupling for enhanced crosstalk suppression", Quantum Science and Technology 9 4, 045003 (2024).
[40] I-Chi Chen, Benjamin Burdick, Yongxin Yao, Peter P. Orth, and Thomas Iadecola, "Error-mitigated simulation of quantum many-body scars on quantum computers with pulse-level control", Physical Review Research 4 4, 043027 (2022).
[41] Eduardo Bayro-Corrochano, Geometric Algebra Applications Vol. III 387 (2024) ISBN:978-3-031-66341-3.
[42] Gokul Subramanian Ravi, Jonathan M. Baker, Arash Fayyazi, Sophia Fuhui Lin, Ali Javadi-Abhari, Massoud Pedram, and Frederic T. Chong, Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 88 (2023) ISBN:9781450399166.
[43] Ryan Shaffer, Lucas Kocia, and Mohan Sarovar, "Surrogate-based optimization for variational quantum algorithms", Physical Review A 107 3, 032415 (2023).
[44] Swarnadeep Majumder, Christopher G. Yale, Titus D. Morris, Daniel S. Lobser, Ashlyn D. Burch, Matthew N. H. Chow, Melissa C. Revelle, Susan M. Clark, and Raphael C. Pooser, "Characterizing and mitigating coherent errors in a trapped ion quantum processor using hidden inverses", Quantum 7, 1006 (2023).
[45] Bharat Thotakura and Tzu-Chieh Wei, "Quantum state transfer: interplay between gate and readout errors", Quantum Information Processing 22 7, 275 (2023).
[46] Noah Goss, Samuele Ferracin, Akel Hashim, Arnaud Carignan-Dugas, John Mark Kreikebaum, Ravi K. Naik, David I. Santiago, and Irfan Siddiqi, "Extending the computational reach of a superconducting qutrit processor", npj Quantum Information 10 1, 101 (2024).
[47] Qingfeng Wang, Liudmila A. Zhukas, Qiang Miao, Aniket S. Dalvi, Peter J. Love, Christopher Monroe, Frederic T. Chong, and Gokul Subramanian Ravi, "An end-to-end workflow for executing a classically bootstrapped variational quantum algorithm on an academic quantum computer", npj Unconventional Computing 3 1, 28 (2026).
[48] Supanut Thanasilp, Samson Wang, M. Cerezo, and Zoë Holmes, "Exponential concentration in quantum kernel methods", Nature Communications 15 1, 5200 (2024).
[49] Ihor Sokolov and Jacek Dziarmaga, "Bang-bang preparation of a quantum many-body ground state in a finite lattice: Optimization of the algorithm with a tensor network", Physical Review B 111 24, 245144 (2025).
[50] Takaharu Yoshida, Yuta Shingu, Chihaya Shimada, Tetsuro Nikuni, Hideaki Hakoshima, and Yuichiro Matsuzaki, "Hardware-efficient quantum annealing with error mitigation via classical shadow", Physical Review A 113 6, 062430 (2026).
[51] Yunfei Wang and Junyu Liu, "A comprehensive review of quantum machine learning: from NISQ to fault tolerance", Reports on Progress in Physics 87 11, 116402 (2024).
[52] Zahar Sayapin, Daniil Rabinovich, Nikita Korolev, and Kirill Lakhmanskiy, "Zero-noise extrapolation via cyclic permutations of quantum circuit layouts", Physical Review A 114 1, 012620 (2026).
[53] Vasily Sazonov and Mohamed Tamaazousti, "Quantum error mitigation for parametric circuits", Physical Review A 105 4, 042408 (2022).
[54] Samson Wang, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Lukasz Cincio, and Patrick J. Coles, "Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?", Quantum 8, 1287 (2024).
[55] Mario Motta, Gavin O. Jones, Julia E. Rice, Tanvi P. Gujarati, Rei Sakuma, Ieva Liepuoniute, Jeannette M. Garcia, and Yu-ya Ohnishi, "Quantum chemistry simulation of ground- and excited-state properties of the sulfonium cation on a superconducting quantum processor", Chemical Science 14 11, 2915 (2023).
[56] Bikram Khanal and Pablo Rivas, "Data-dependent generalization bounds for parameterized quantum models under noise", The Journal of Supercomputing 81 4, 611 (2025).
[57] Michael Krebsbach, Björn Trauzettel, and Alessio Calzona, "Optimization of Richardson extrapolation for quantum error mitigation", Physical Review A 106 6, 062436 (2022).
[58] Junyao Zhang, Hanrui Wang, Gokul Subramanian Ravi, Frederic T. Chong, Song Han, Frank Mueller, and Yiran Chen, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 1062 (2023) ISBN:979-8-3503-4323-6.
[59] Vincent Russo and Andrea Mari, "Quantum error mitigation by layerwise Richardson extrapolation", Physical Review A 110 6, 062420 (2024).
[60] Yabo Wang, Bo Qi, Xin Wang, Tongliang Liu, and Daoyi Dong, "Power Characterization of Noisy Quantum Kernels", IEEE Transactions on Neural Networks and Learning Systems 36 8, 13939 (2025).
[61] Yusuke Hama and Hirofumi Nishi, "Quantum error mitigation via quantum-noise-effect circuit groups", Scientific Reports 14 1, 6077 (2024).
[62] Karl Michael Ziems, Erik Rosendahl Kjellgren, Stephan P. A. Sauer, Jacob Kongsted, and Sonia Coriani, "Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers", Chemical Science 16 10, 4456 (2025).
[63] Ashutosh Tiwari, Zian Wang, and Himanshu Gupta, 2026 International Conference on Quantum Communications, Networking, and Computing (QCNC) 676 (2026) ISBN:979-8-3315-6110-9.
[64] Josu Etxezarreta Martinez, Olatz Sanz Larrarte, Javier Oliva del Moral, Reza Dastbasteh, and Ruben M. Otxoa, "Comment on “Recovering noise-free quantum observables”", Physical Review A 110 4, 046401 (2024).
[65] Chi-Chou Kao and Hung-Yi Lin, "Performance-Oriented Layout Synthesis for Quantum Computing", Computer Systems Science and Engineering 48 6, 1581 (2024).
[66] Erik Lötstedt and Kaoru Yamanouchi, Topics in Applied Physics 151, 137 (2024) ISBN:978-3-031-55462-9.
[67] Clemens Lindner, Joonas Hämäläinen, and Matti Raasakka, Communications in Computer and Information Science 2743, 301 (2026) ISBN:978-3-032-13851-4.
[68] Benchen Huang, Marco Govoni, and Giulia Galli, "Simulating the Electronic Structure of Spin Defects on Quantum Computers", PRX Quantum 3 1, 010339 (2022).
[69] Renato M.S. Farias, Thiago O. Maciel, Giancarlo Camilo, Ruge Lin, Sergi Ramos-Calderer, and Leandro Aolita, "Quantum encoder for fixed-Hamming-weight subspaces", Physical Review Applied 23 4, 044014 (2025).
[70] Chunhui Zhang, Feng Xu, Shihang Zhang, Mingchao Duan, Dupeng Zhong, Xuesong Bai, Hao Wang, Chao Huang, Yi Deng, Miao Gao, Yu-Ning Zhang, Jiaze Liu, Chunhui Li, Yan Jiang, Baolong Zhao, Huan Shu, Kunrong Wu, Keji Shi, Qiming Ding, Zhen Tian, Guanyong Wang, Xiao Yuan, Tao Xin, Guangchong Hu, Song Liu, Tianluo Pan, Peihao Huang, Yu He, and Dapeng Yu, "Universal logical operations in a silicon quantum processor", Nature Nanotechnology 21 5, 635 (2026).
[71] Michael A. Jones, Harish J. Vallury, and Lloyd C.L. Hollenberg, "Ground-state-energy calculation for the water molecule on a superconducting quantum processor", Physical Review Applied 21 6, 064017 (2024).
[72] Zongkang Zhang, Yongdan Yang, Xiaosi Xu, and Ying Li, "Quantum algorithms for Schrieffer-Wolff transformation", Physical Review Research 4 4, 043023 (2022).
[73] Victor Martinez, Omar Fawzi, and Daniel Stilck França, "Sampling (noisy) quantum circuits through randomized rounding", Quantum 10, 2068 (2026).
[74] Shuo Liu, Shao-Kai Jian, and Shi-Xin Zhang, "Noisy monitored quantum circuits", Journal of Physics: Condensed Matter 38 20, 203001 (2026).
[75] Sahil Gulania, Yuri Alexeev, Stephen K. Gray, Bo Peng, and Niranjan Govind, "Quantum Time Dynamics Mediated by the Yang–Baxter Equation and Artificial Neural Networks", Journal of Chemical Theory and Computation 21 13, 6280 (2025).
[76] Ryuji Takagi, Suguru Endo, Shintaro Minagawa, and Mile Gu, "Fundamental limits of quantum error mitigation", npj Quantum Information 8 1, 114 (2022).
[77] Samuel Sepúlveda, Ricardo Pérez-Castillo, and Mario Piattini, Anais do XXVIII Congresso Ibero-Americano em Engenharia de Software (CIbSE 2025) 60 (2025).
[78] Laura M. Donaire, Gloria Ortega, Ester M. Garzón, and Francisco Orts, "Lowering the cost of quantum comparator circuits", The Journal of Supercomputing 80 10, 13900 (2024).
[79] Wenbo Shi, Neel Kanth Kundu, Matthew R. McKay, and Robert Malaney, 2025 International Conference on Quantum Communications, Networking, and Computing (QCNC) 32 (2025) ISBN:979-8-3315-3159-1.
[80] C. Huerta Alderete, Alaina M. Green, Nhung H. Nguyen, Yingyue Zhu, Norbert M. Linke, and B. M. Rodríguez-Lara, "Para-particle oscillator simulations on a trapped-ion quantum computer", Journal of Applied Physics 138 5, 054401 (2025).
[81] Hang Zou, Erika Magnusson, Hampus Brunander, Werner Dobrautz, and Martin Rahm, "Multireference error mitigation for quantum computation of chemistry", Digital Discovery 4 9, 2521 (2025).
[82] Yifeng Xiong, Daryus Chandra, Soon Xin Ng, and Lajos Hanzo, "Circuit Symmetry Verification Mitigates Quantum-Domain Impairments", IEEE Transactions on Signal Processing 71, 477 (2023).
[83] Yousung Kang and Kyungsun Moon, "Effective Hamiltonian and parametric tuning for the cross-cross-resonance gate in the transmon model", Physical Review Applied 23 1, 014062 (2025).
[84] Sorana Catrina and Alexandra Băicoianu, "Quantum Tunneling: From Theory to Error‐Mitigated Quantum Simulation", Advanced Quantum Technologies 8 1, 2400163 (2025).
[85] Pradeep Niroula, Sarang Gopalakrishnan, and Michael J. Gullans, "Error mitigation thresholds in noisy random quantum circuits", Physical Review B 112 2, 024206 (2025).
[86] Yuri Alexeev, Marwa H. Farag, Taylor L. Patti, Mark E. Wolf, Natalia Ares, Alán Aspuru-Guzik, Simon C. Benjamin, Zhenyu Cai, Shuxiang Cao, Christopher Chamberland, Zohim Chandani, Federico Fedele, Ikko Hamamura, Nicholas Harrigan, Jin-Sung Kim, Elica Kyoseva, Justin G. Lietz, Tom Lubowe, Alexander McCaskey, Roger G. Melko, Kouhei Nakaji, Alberto Peruzzo, Pooja Rao, Bruno Schmitt, Sam Stanwyck, Norm M. Tubman, Hanrui Wang, and Timothy Costa, "Artificial intelligence for quantum computing", Nature Communications 16 1, 10829 (2025).
[87] Srikar Kasi, James Sud, Kyle Jamieson, and Gokul Subramanian Ravi, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 368 (2024) ISBN:979-8-3315-4137-8.
[88] Yihui Quek, Daniel Stilck França, Sumeet Khatri, Johannes Jakob Meyer, and Jens Eisert, "Exponentially tighter bounds on limitations of quantum error mitigation", Nature Physics 20 10, 1648 (2024).
[89] Hossam Ahmed, Burak Mete, Helmut Heller, Matthew Tovey, Xiaolong Deng, Asim Zulfiqar, Muhammad Nufail Farooqi, Mahmoud Abuzayed, Martin Schulz, and Laura Schulz, ISC High Performance 2025 Research Paper Proceedings (40th International Conference) 1 (2025) ISBN:978-3-9826336-1-9.
[90] Vincent R. Pascuzzi, Andre He, Christian W. Bauer, Wibe A. de Jong, and Benjamin Nachman, "Computationally efficient zero-noise extrapolation for quantum-gate-error mitigation", Physical Review A 105 4, 042406 (2022).
[91] Hoang-Quan Nguyen, Xuan Bac Nguyen, Samuel Yen-Chi Chen, Hugh Churchill, Nicholas Borys, Samee U. Khan, and Khoa Luu, "Diffusion-inspired quantum noise mitigation in parameterized quantum circuits", Quantum Machine Intelligence 7 1, 55 (2025).
[92] Wladimir Silva and Frank Mueller, 2026 IEEE International Parallel and Distributed Processing Symposium (IPDPS) 942 (2026) ISBN:979-8-3195-0602-3.
[93] Viki Kumar Prasad, Freeman Cheng, Ulrich Fekl, and Hans-Arno Jacobsen, "Applications of noisy quantum computing and quantum error mitigation to “adamantaneland”: a benchmarking study for quantum chemistry", Physical Chemistry Chemical Physics 26 5, 4071 (2024).
[94] Samuele Ferracin, Akel Hashim, Jean-Loup Ville, Ravi Naik, Arnaud Carignan-Dugas, Hammam Qassim, Alexis Morvan, David I. Santiago, Irfan Siddiqi, and Joel J. Wallman, "Efficiently improving the performance of noisy quantum computers", Quantum 8, 1410 (2024).
[95] Anna Schroeder, Matthias Heller, and Mariami Gachechiladze, "Deterministic Ansätze for the measurement-based variational quantum eigensolver", New Journal of Physics 26 6, 063019 (2024).
[96] Vincent Russo, Andrea Mari, Nathan Shammah, Ryan LaRose, and William J. Zeng, "Testing Platform-Independent Quantum Error Mitigation on Noisy Quantum Computers", IEEE Transactions on Quantum Engineering 4, 1 (2023).
[97] Xiongzhi Zeng, Yi Fan, Jie Liu, Zhenyu Li, and Jinlong Yang, "Quantum Neural Network Inspired Hardware Adaptable Ansatz for Efficient Quantum Simulation of Chemical Systems", Journal of Chemical Theory and Computation 19 23, 8587 (2023).
[98] Matteo Robbiati, Alejandro Sopena, Andrea Papaluca, and Stefano Carrazza, "Real-time error mitigation for variational optimization on quantum hardware", Physical Review Research 8 1, 013262 (2026).
[99] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien, "Quantum error mitigation", Reviews of Modern Physics 95 4, 045005 (2023).
[100] Youngseok Kim, Christopher J. Wood, Theodore J. Yoder, Seth T. Merkel, Jay M. Gambetta, Kristan Temme, and Abhinav Kandala, "Scalable error mitigation for noisy quantum circuits produces competitive expectation values", Nature Physics 19 5, 752 (2023).
[101] Unai Aseguinolaza, Nahual Sobrino, Gabriel Sobrino, Joaquim Jornet-Somoza, and Juan Borge, "Error estimation in current noisy quantum computers", Quantum Information Processing 23 5, 181 (2024).
[102] Rawad Mezher, James Mills, and Elham Kashefi, "Mitigating errors by quantum verification and postselection", Physical Review A 105 5, 052608 (2022).
[103] Jiaxin Li, Zhaobing Fan, Hongmei Yao, Chunlin Yang, Shao-Ming Fei, Zi-Tong Zhou, Meng-Han Dou, and Teng-Yang Ma, "Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems", Physical Review A 113 1, 012406 (2026).
[104] Laura M. Donaire, Gloria Ortega, Francisco Orts, and Ester M. Garzón, Lecture Notes in Computer Science 15385, 64 (2025) ISBN:978-3-031-90199-7.
[105] Yuxuan Du, Tao Huang, Shan You, Min-Hsiu Hsieh, and Dacheng Tao, "Quantum circuit architecture search for variational quantum algorithms", npj Quantum Information 8 1, 62 (2022).
[106] Erik Lötstedt, Kaoru Yamanouchi, and Yutaka Tachikawa, "Evaluation of vibrational energies and wave functions of CO2 on a quantum computer", AVS Quantum Science 4 3, 036801 (2022).
[107] V. Karthick, D. Lakshanya, and P. Nandha Kumar, "Enhancing quantum computation accuracy on IBM quantum hardware through advanced error mitigation strategies", Discover Quantum Science 2 1, 16 (2026).
[108] Anirban Mukherjee, Noah F. Berthusen, João C. Getelina, Peter P. Orth, and Yong-Xin Yao, "Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models", Communications Physics 6 1, 4 (2023).
[109] Temitope Bolaji Adeniyi and Sathish A. P. Kumar, "Adaptive neural network for quantum error mitigation", Quantum Machine Intelligence 7 1, 13 (2025).
[110] Chien-Hung Cho, Chih-Yu Chen, Kuo-Chin Chen, Tsung-Wei Huang, Ming-Chien Hsu, Ning-Ping Cao, Bei Zeng, Seng-Ghee Tan, and Ching-Ray Chang, "Quantum computation: Algorithms and Applications", Chinese Journal of Physics 72, 248 (2021).
[111] Nacer Eddine Belaloui, Abdellah Tounsi, Abdelmouheymen Rabah Khamadja, Mohamed Messaoud Louamri, Achour Benslama, David E. Bernal Neira, and Mohamed Taha Rouabah, "Ground-State Energy Estimation on Current Quantum Hardware through the Variational Quantum Eigensolver: A Practical Study", Journal of Chemical Theory and Computation 21 14, 6777 (2025).
[112] Boseon Kim, Wooyeong Song, Kwangil Bae, Wonhyuk Lee, and IlKwon Sohn, "Enhanced extrapolation-based quantum error mitigation using repetitive structure in quantum algorithms", Quantum Science and Technology 11 3, 035037 (2026).
[113] Paula García-Molina, Ana Martin, Mikel Garcia de Andoin, and Mikel Sanz, "Mitigating noise in digital and digital–analog quantum computation", Communications Physics 7 1, 321 (2024).
[114] Phattharaporn Singkanipa and Daniel A. Lidar, "Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets", Quantum 9, 1617 (2025).
[115] He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long, "Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation", Science China Physics, Mechanics & Astronomy 66 5, 250302 (2023).
[116] Sandeep Kumar Sood, Manmohan Singh, and Munish Bhatia, "Industrial progress with quantum algorithms: an in-depth review", The Journal of Supercomputing 81 9, 1064 (2025).
[117] Wentao Chen, Shuaining Zhang, Jialiang Zhang, Xiaolu Su, Yao Lu, Kuan Zhang, Mu Qiao, Ying Li, Jing-Ning Zhang, and Kihwan Kim, "Error-mitigated quantum simulation of interacting fermions with trapped ions", npj Quantum Information 9 1, 122 (2023).
[118] Takanori Nishi and Kaoru Yamanouchi, "Simulation of a spin-boson model by iterative optimization of a parametrized quantum circuit", AVS Quantum Science 6 2, 023801 (2024).
[119] Cristina Cirstoiu, Silas Dilkes, Daniel Mills, Seyon Sivarajah, and Ross Duncan, "Volumetric Benchmarking of Error Mitigation with Qermit", Quantum 7, 1059 (2023).
[120] Soumen Pal, Manojit Bhattacharya, Snehasish Dash, Sang-Soo Lee, and Chiranjib Chakraborty, "Future Potential of Quantum Computing and Simulations in Biological Science", Molecular Biotechnology 66 9, 2201 (2024).
[121] Arefur Rahman, Daniel J. Egger, and Christian Arenz, "Learning how to dynamically decouple by optimizing rotational gates", Physical Review Applied 22 5, 054074 (2024).
[122] Yue Ruan, Zhiqiang Yuan, Xiling Xue, and Zhihao Liu, "Quantum approximate optimization for combinatorial problems with constraints", Information Sciences 619, 98 (2023).
[123] Hrushikesh Pramod Patil, Dror Baron, and Huiyang Zhou, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 849 (2025) ISBN:979-8-3315-5736-2.
[124] Alistair W. R. Smith, Kiran E. Khosla, Chris N. Self, and M. S. Kim, "Qubit readout error mitigation with bit-flip averaging", Science Advances 7 47, eabi8009 (2021).
[125] Juan Borge, Unai Aseguinolaza, Nahual Sobrino, Gabriel Sobrino, and Joaquim Jornet-Somoza, "Error Estimation in Current Noisy Quantum Computers", (2023).
[126] Mingxia Huo and Ying Li, "Dual-state purification for practical quantum error mitigation", Physical Review A 105 2, 022427 (2022).
[127] Yuki Takeuchi, Yasuhiro Takahashi, Tomoyuki Morimae, and Seiichiro Tani, "Divide-and-conquer verification method for noisy intermediate-scale quantum computation", Quantum 6, 758 (2022).
[128] Asmar Muqeet, Shaukat Ali, Tao Yue, and Paolo Arcaini, Companion Proceedings of the 32nd ACM International Conference on the Foundations of Software Engineering 80 (2024) ISBN:9798400706585.
[129] Daniel Bultrini, Max Hunter Gordon, Esperanza López, and Germán Sierra, "Simple Mitigation Strategy for a Systematic Gate Error in IBMQ", Journal of Applied Mathematics and Physics 09 06, 1215 (2021).
[130] Frédéric Sauvage, Martín Larocca, Patrick J Coles, and M Cerezo, "Building spatial symmetries into parameterized quantum circuits for faster training", Quantum Science and Technology 9 1, 015029 (2024).
[131] Shi-Xin Zhang and Shuai Yin, "Universal imaginary-time critical dynamics on a quantum computer", Physical Review B 109 13, 134309 (2024).
[132] Shuanghong Tang, Congcong Zheng, and Kun Wang, "Detecting and eliminating quantum noise of quantum measurements", Physica Scripta 99 10, 105129 (2024).
[133] Lorcán O. Conlon, Tobias Vogl, Christian D. Marciniak, Ivan Pogorelov, Simon K. Yung, Falk Eilenberger, Dominic W. Berry, Fabiana S. Santana, Rainer Blatt, Thomas Monz, Ping Koy Lam, and Syed M. Assad, "Approaching optimal entangling collective measurements on quantum computing platforms", Nature Physics 19 3, 351 (2023).
[134] Hugo Perrin, Thibault Scoquart, Alexander Shnirman, Jörg Schmalian, and Kyrylo Snizhko, "Mitigating crosstalk errors by randomized compiling: Simulation of the BCS model on a superconducting quantum computer", Physical Review Research 6 1, 013142 (2024).
[135] Jose D. Guimaraes and Carlos Tavares, 2022 IEEE International Conference on Quantum Software (QSW) 41 (2022) ISBN:978-1-6654-8134-2.
[136] Emanuele Costa, Axel Pérez-Obiol, Javier Menéndez, Arnau Rios, Artur García-Sáez, and Bruno Juliá-Díaz, "Quasiparticle pairing encoding of atomic nuclei for quantum annealing", Physics Letters B 872, 140042 (2026).
[137] Alisa Haukisalmi, Daniel Paz Ramos, Matti Raasakka, Andrea Marchesin, Lauri Ylinen, and Ilkka Tittonen, "Noisy quantum simulation: Performance and resource considerations for the Tavis-Cummings and Heisenberg models", Physical Review Research 7 4, 043254 (2025).
[138] Gideon Lee, Connor T. Hann, Shruti Puri, S. M. Girvin, and Liang Jiang, "Error Suppression for Arbitrary-Size Black Box Quantum Operations", Physical Review Letters 131 19, 190601 (2023).
[139] Gabriel Pontolillo, Asmar Muqeet, Shaukat Ali, and Mohammad Reza Mousavi, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 405 (2025) ISBN:979-8-3315-5736-2.
[140] Yoshinori Ato, Yutaka Tachikawa, Ryuhei Yoshida, Erik Lötstedt, and Kaoru Yamanouchi, "Quantum computing of Hückel molecular orbitals of linear polyenes", Chemical Physics Letters 877, 142276 (2025).
[141] Mario Motta, Kevin J. Sung, and James Shee, "Quantum Algorithms for the Variational Optimization of Correlated Electronic States with Stochastic Reconfiguration and the Linear Method", The Journal of Physical Chemistry A 128 40, 8762 (2024).
[142] Thierry N. Kaldenbach, Matthias Heller, Gernot Alber, and Vladimir M. Stojanović, "Digital Quantum Simulation of Scalar Yukawa Coupling", Quantum Reports 6 3, 366 (2024).
[143] Akash Kundu, "Improving thermal state preparation of Sachdev–Ye–Kitaev model with reinforcement learning on quantum hardware", Machine Learning: Science and Technology 6 2, 025066 (2025).
[144] Ben Bar, Jader P. Santos, and Raam Uzdin, "Layered KIK quantum error mitigation for dynamic circuits", npj Quantum Information 12 1, 79 (2026).
[145] Thomas Steckmann, Trevor Keen, Efekan Kökcü, Alexander F. Kemper, Eugene F. Dumitrescu, and Yan Wang, "Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer", Physical Review Research 5 2, 023198 (2023).
[146] Gokul Subramanian Ravi, Jonathan M. Baker, Kaitlin N. Smith, Nathan Earnest, Ali Javadi-Abhari, and Frederic T. Chong, 2022 IEEE International Conference on Rebooting Computing (ICRC) 66 (2022) ISBN:979-8-3503-4709-8.
[147] Aroosa Ijaz, C. Huerta Alderete, Frédéric Sauvage, Lukasz Cincio, M. Cerezo, and Matthew L. Goh, "More buck-per-shot: Why learning trumps mitigation in noisy quantum sensing", Materials Today Quantum 6, 100042 (2025).
[148] Shichuan Xue, Guangyao Huang, Yong Liu, Dongyang Wang, Weixu Shi, Yingwen Liu, Xiang Fu, Anqi Huang, Mingtang Deng, and Junjie Wu, "Efficient quantum process tomography for Clifford circuits", Physical Review A 108 3, 032419 (2023).
[149] Kausthubh Chandramouli, Kelly Mae Allen, Christopher Mori, Dror Baron, and Mário A. T. Figueiredo, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 269 (2025) ISBN:979-8-3315-5736-2.
[150] Francisco Orts, Gloria Ortega, Ernestas Filatovas, and Ester M. Garzón, "Implementation of three efficient 4-digit fault-tolerant quantum carry lookahead adders", The Journal of Supercomputing 78 11, 13323 (2022).
[151] Dax Enshan Koh and Sabee Grewal, "Classical Shadows With Noise", Quantum 6, 776 (2022).
[152] Hiroshi Ohno, "Adaptive pruning algorithm using a quantum Fisher information matrix for parameterized quantum circuits", Quantum Machine Intelligence 6 2, 77 (2024).
[153] Timon Scheiber, Paul Haubenwallner, and Matthias Heller, "Reduced Sampling Overhead for Probabilistic Error Cancellation by Pauli Error Propagation", Quantum 9, 1840 (2025).
[154] Vu Tuan Hai, Jesus Urbaneja, and Le Bin Ho, 2025 IEEE International Conference on Quantum Software (QSW) 116 (2025) ISBN:979-8-3315-6720-0.
[155] Erik Lötstedt, Takanori Nishi, and Kaoru Yamanouchi, "Simulation of time-dependent quantum dynamics using quantum computers", Advances in Atomic Molecular and Optical Physics Advances In Atomic, Molecular, and Optical Physics 73, 33 (2024) ISBN:9780443314582.
[156] Hiroshi Ohno, "A direct error correction method for quantum machine learning", Quantum Information Processing 22 2, 119 (2023).
[157] Danila Babukhin, "Echo-evolution data generation for quantum error mitigation via neural networks", Quantum Information Processing 23 12, 405 (2024).
[158] Xiao-Dao Lin, Hsi-Ming Chang, Jhih-Shih You, and Hsiu-Chuan Hsu, 2025 IEEE International Conference on Quantum Control, Computing and Learning (qCCL) 58 (2025) ISBN:978-1-6654-5782-8.
[159] Nick S. Blunt, Laura Caune, Róbert Izsák, Earl T. Campbell, and Nicole Holzmann, "Statistical Phase Estimation and Error Mitigation on a Superconducting Quantum Processor", PRX Quantum 4 4, 040341 (2023).
[160] Yuxuan Zhang, Daoheng Niu, Alireza Shabani, and Hassan Shapourian, "Quantum Volume for Photonic Quantum Processors", Physical Review Letters 130 11, 110602 (2023).
[161] T. A. Cochran, B. Jobst, E. Rosenberg, Y. D. Lensky, G. Gyawali, N. Eassa, M. Will, A. Szasz, D. Abanin, R. Acharya, L. Aghababaie Beni, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Babbush, B. Ballard, J. C. Bardin, A. Bengtsson, A. Bilmes, A. Bourassa, J. Bovaird, M. Broughton, D. A. Browne, B. Buchea, B. B. Buckley, T. Burger, B. Burkett, N. Bushnell, A. Cabrera, J. Campero, H.-S. Chang, Z. Chen, B. Chiaro, J. Claes, A. Y. Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, S. Das, S. Demura, L. De Lorenzo, A. Di Paolo, P. Donohoe, I. Drozdov, A. Dunsworth, A. Eickbusch, A. Moshe Elbag, M. Elzouka, C. Erickson, V. S. Ferreira, L. Flores Burgos, E. Forati, A. G. Fowler, B. Foxen, S. Ganjam, R. Gasca, É. Genois, W. Giang, D. Gilboa, R. Gosula, A. Grajales Dau, D. Graumann, A. Greene, J. A. Gross, S. Habegger, M. Hansen, M. P. Harrigan, S. D. Harrington, P. Heu, O. Higgott, J. Hilton, H.-Y. Huang, A. Huff, W. Huggins, E. Jeffrey, Z. Jiang, C. Jones, C. Joshi, P. Juhas, D. Kafri, H. Kang, A. H. Karamlou, K. Kechedzhi, T. Khaire, T. Khattar, M. Khezri, S. Kim, P. Klimov, B. Kobrin, A. Korotkov, F. Kostritsa, J. Kreikebaum, V. Kurilovich, D. Landhuis, T. Lange-Dei, B. Langley, K.-M. Lau, J. Ledford, K. Lee, B. Lester, L. Le Guevel, W. Li, A. T. Lill, W. Livingston, A. Locharla, D. Lundahl, A. Lunt, S. Madhuk, A. Maloney, S. Mandrà, L. Martin, O. Martin, C. Maxfield, J. McClean, M. McEwen, S. Meeks, A. Megrant, K. Miao, R. Molavi, S. Molina, S. Montazeri, R. Movassagh, C. Neill, M. Newman, A. Nguyen, M. Nguyen, C.-H. Ni, K. Ottosson, A. Pizzuto, R. Potter, O. Pritchard, C. Quintana, G. Ramachandran, M. Reagor, D. Rhodes, G. Roberts, K. Sankaragomathi, K. Satzinger, H. Schurkus, M. Shearn, A. Shorter, N. Shutty, V. Shvarts, V. Sivak, S. Small, W. C. Smith, S. Springer, G. Sterling, J. Suchard, A. Sztein, D. Thor, M. Torunbalci, A. Vaishnav, J. Vargas, S. Vdovichev, G. Vidal, C. Vollgraff Heidweiller, S. Waltman, S. X. Wang, B. Ware, T. White, K. Wong, B. W. K. Woo, C. Xing, Z. Jamie Yao, P. Yeh, B. Ying, J. Yoo, N. Yosri, G. Young, A. Zalcman, Y. Zhang, N. Zhu, N. Zobrist, S. Boixo, J. Kelly, E. Lucero, Y. Chen, V. Smelyanskiy, H. Neven, A. Gammon-Smith, F. Pollmann, M. Knap, and P. Roushan, "Visualizing dynamics of charges and strings in (2 + 1)D lattice gauge theories", Nature 642 8067, 315 (2025).
[162] Phat Thanh Tran, Ryan Carmichael, Jake Scally, Austin Myers, Huynjin Yi, Xiuwen Liu, and Bayaner Arigong, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 2057 (2025) ISBN:979-8-3315-5736-2.
[163] Jin Ming Koh, Dax Enshan Koh, and Jayne Thompson, "Readout Error Mitigation for Mid-Circuit Measurements and Feedforward", PRX Quantum 7 1, 010317 (2026).
[164] Erik Lötstedt and Kaoru Yamanouchi, "Comparison of current quantum devices for quantum computing of Heisenberg spin chain dynamics", Chemical Physics Letters 836, 140975 (2024).
[165] Amara Katabarwa, Katerina Gratsea, Athena Caesura, and Peter D. Johnson, "Early Fault-Tolerant Quantum Computing", PRX Quantum 5 2, 020101 (2024).
[166] Stefan H. Sack and Daniel J. Egger, "Large-scale quantum approximate optimization on nonplanar graphs with machine learning noise mitigation", Physical Review Research 6 1, 013223 (2024).
[167] Dror Baron, Hrushikesh Pramod Patil, and Huiyang Zhou, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 124 (2024) ISBN:979-8-3315-4137-8.
[168] Samson Wang, Enrico Fontana, M. Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J. Coles, "Noise-induced barren plateaus in variational quantum algorithms", Nature Communications 12 1, 6961 (2021).
[169] Piotr Czarnik, Michael McKerns, Andrew T. Sornborger, and Lukasz Cincio, "Improving the efficiency of learning-based error mitigation", Quantum 9, 1727 (2025).
[170] Aosai Zhang, Haipeng Xie, Yu Gao, Jia-Nan Yang, Zehang Bao, Zitian Zhu, Jiachen Chen, Ning Wang, Chuanyu Zhang, Jiarun Zhong, Shibo Xu, Ke Wang, Yaozu Wu, Feitong Jin, Xuhao Zhu, Yiren Zou, Ziqi Tan, Zhengyi Cui, Fanhao Shen, Tingting Li, Yihang Han, Yiyang He, Gongyu Liu, Jiayuan Shen, Han Wang, Yanzhe Wang, Hang Dong, Jinfeng Deng, Hekang Li, Zhen Wang, Chao Song, Qiujiang Guo, Pengfei Zhang, Ying Li, and H. Wang, "Demonstrating quantum error mitigation on logical qubits", Nature Communications 17 1, 1021 (2025).
[171] Andrey Zhukov and Walter Pogosov, "Quantum error reduction with deep neural network applied at the post-processing stage", Quantum Information Processing 21 3, 93 (2022).
[172] Takanori Nishi, Erik Lötstedt, and Kaoru Yamanouchi, "Simulation of a laser-driven three-level system by a noisy quantum computer", AVS Quantum Science 4 4, 043801 (2022).
[173] Alireza Seif, Ze-Pei Cian, Sisi Zhou, Senrui Chen, and Liang Jiang, "Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors", PRX Quantum 4 1, 010303 (2023).
[174] Lajos Hanzo, Zunaira Babar, Zhenyu Cai, Daryus Chandra, Ivan B. Djordjevic, Balint Koczor, Soon Xin Ng, Mohsen Razavi, and Osvaldo Simeone, "Quantum Information Processing, Sensing, and Communications: Their Myths, Realities, and Futures", Proceedings of the IEEE 113 9, 1024 (2025).
[175] Matthew L. Goh, Martin Larocca, Lukasz Cincio, M. Cerezo, and Frédéric Sauvage, "Lie-algebraic classical simulations for quantum computing", Physical Review Research 7 3, 033266 (2025).
[176] Jordi Pérez-Guijarro, Alba Pagès-Zamora, and Javier R. Fonollosa, "Extension of Clifford Data Regression Methods for Quantum Error Mitigation", IEEE Transactions on Quantum Engineering 7, 1 (2026).
[177] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles, "Variational quantum algorithms", Nature Reviews Physics 3 9, 625 (2021).
[178] Ryuji Takagi, Hiroyasu Tajima, and Mile Gu, "Universal Sampling Lower Bounds for Quantum Error Mitigation", Physical Review Letters 131 21, 210602 (2023).
[179] Xiaochuan Ding and Bryan K. Clark, "Classical postprocessing for the unitary block-optimization scheme to reduce the effect of noise on the optimization of variational quantum eigensolvers", Physical Review A 110 6, 062403 (2024).
[180] Siddharth Dangwal, Gokul Subramanian Ravi, Poulami Das, Kaitlin N. Smith, Jonathan Mark Baker, and Frederic T. Chong, Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 4 362 (2023) ISBN:9798400703942.
[181] Kun Wang, Yu-Ao Chen, and Xin Wang, "Mitigating quantum errors via truncated Neumann series", Science China Information Sciences 66 8, 180508 (2023).
[182] Manwen Liao, Yan Zhu, Giulio Chiribella, and Yuxiang Yang, "Noise-agnostic quantum error mitigation with data augmented neural models", npj Quantum Information 11 1, 8 (2025).
[183] M. Cerezo, Guillaume Verdon, Hsin-Yuan Huang, Lukasz Cincio, and Patrick J. Coles, "Challenges and opportunities in quantum machine learning", Nature Computational Science 2 9, 567 (2022).
[184] Ryan LaRose, Andrea Mari, Sarah Kaiser, Peter J. Karalekas, Andre A. Alves, Piotr Czarnik, Mohamed El Mandouh, Max H. Gordon, Yousef Hindy, Aaron Robertson, Purva Thakre, Misty Wahl, Danny Samuel, Rahul Mistri, Maxime Tremblay, Nick Gardner, Nathaniel T. Stemen, Nathan Shammah, and William J. Zeng, "Mitiq: A software package for error mitigation on noisy quantum computers", Quantum 6, 774 (2022).
[185] J.-Z. Zhuang, Y.-K. Wu, and L.-M. Duan, "Hardware-efficient variational quantum algorithm in a trapped-ion quantum computer", Physical Review A 110 6, 062414 (2024).
[186] Elijah Pelofske and Vincent Russo, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 01 (2025) ISBN:979-8-3315-5736-2.
[187] Bo Yang, Nobuyuki Yoshioka, Hiroyuki Harada, Shigeo Hakkaku, Yuuki Tokunaga, Hideaki Hakoshima, Kaoru Yamamoto, and Suguru Endo, "Resource-efficient generalized quantum subspace expansion", Physical Review Applied 23 5, 054021 (2025).
[188] Michael A. Jones, Harish J. Vallury, Manolo C. Per, Harry M. Quiney, and Lloyd C. L. Hollenberg, "Moments-based improved quantum computation of the electric dipole moment of molecular systems", Physical Review Applied 25 5, 054001 (2026).
[189] Peiyi Li, Ji Liu, Alvin Gonzales, Zain Hamid Saleem, Huiyang Zhou, and Paul Hovland, 2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA) 103 (2024) ISBN:979-8-3503-2658-1.
[190] Mateusz Przygocki, Rafał Kotas, and Mariusz Zubert, 2026 33rd International Conference on Mixed Design of Integrated Circuits and System (MIXDES) 370 (2026) ISBN:978-83-63578-30-5.
[191] Seid Koudia, Leonardo Oleynik, Mert Bayraktar, Junaid Ur Rehman, and Symeon Chatzinotas, "Physical-Layer Aspects of Quantum Communications: A Survey", IEEE Communications Surveys & Tutorials 28, 4429 (2026).
[192] Dhanvi Bharadwaj, Yuewen Hou, Alexander Knapen, Gino Kwun, Nikolai Zhitkov, and Gokul Subramanian Ravi, Communications in Computer and Information Science 2724, 148 (2026) ISBN:978-981-95-7828-3.
[193] Maksym Prodius, Piotr Czarnik, Michael McKerns, Andrew T. Sornborger, and Lukasz Cincio, "Robust Design Under Uncertainty in Quantum Error Mitigation", IEEE Transactions on Quantum Engineering 7, 1 (2026).
[194] Haoran Liao, Derek S. Wang, Iskandar Sitdikov, Ciro Salcedo, Alireza Seif, and Zlatko K. Minev, "Machine learning for practical quantum error mitigation", Nature Machine Intelligence 6 12, 1478 (2024).
[195] Bikrant Bhattacharyya and Gokul Subramanian Ravi, 2023 IEEE International Conference on Rebooting Computing (ICRC) 1 (2023) ISBN:979-8-3503-8204-4.
[196] Angela Rosy Morgillo, Stefano Mangini, Marco Piastra, and Chiara Macchiavello, "Quantum state reconstruction in a noisy environment via deep learning", Quantum Machine Intelligence 6 2, 39 (2024).
[197] Yanzhang Zhu, Siyuan Niu, and Di Wu, 2024 IEEE 6th International Conference on Trust, Privacy and Security in Intelligent Systems, and Applications (TPS-ISA) 489 (2024) ISBN:979-8-3503-8674-5.
[198] Pontus Vikstål, Giulia Ferrini, and Shruti Puri, "Study of noise in virtual distillation circuits for quantum error mitigation", Quantum 8, 1441 (2024).
[199] Poulami Das, Eric Kessler, and Yunong Shi, 2023 IEEE International Symposium on High-Performance Computer Architecture (HPCA) 787 (2023) ISBN:978-1-6654-7652-2.
[200] Smik Patel, Praveen Jayakumar, Tzu-Ching Yen, and Artur F. Izmaylov, "Quantum Measurement for Quantum Chemistry on a Quantum Computer", Chemical Reviews 125 16, 7490 (2025).
[201] Yoga A. Darmawan, Angga D. Fauzi, Yanoar P. Sarwono, and Rui-Qin Zhang, "Improving qubit reduction for molecular simulations with randomized orbital sampling", AAPPS Bulletin 35 1, 27 (2025).
[202] Yifeng Xiong, Soon Xin Ng, and Lajos Hanzo, "Quantum Error Mitigation Relying on Permutation Filtering", IEEE Transactions on Communications 70 3, 1927 (2022).
[203] Erik Lötstedt, Lidong Wang, Ryuhei Yoshida, Youyuan Zhang, and Kaoru Yamanouchi, "Error-mitigated quantum computing of Heisenberg spin chain dynamics", Physica Scripta 98 3, 035111 (2023).
[204] Srushti Patil, Dibyendu Mondal, and Rahul Maitra, "Machine learning approach toward quantum error mitigation for accurate molecular energetics", The Journal of Chemical Physics 163 2, 024129 (2025).
[205] Eliott Rosenberg, Paul Ginsparg, and Peter L McMahon, "Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits", Quantum Science and Technology 7 1, 015024 (2022).
[206] F. Orts, E. Filatovas, G. Ortega, J. F. SanJuan-Estrada, and E. M. Garzón, "Improving the number of T gates and their spread in integer multipliers on quantum computing", Physical Review A 107 4, 042621 (2023).
[207] Alexey Uvarov, Daniil Rabinovich, Olga Lakhmanskaya, Kirill Lakhmanskiy, Jacob Biamonte, and Soumik Adhikary, "Mitigating quantum gate errors for variational eigensolvers using hardware-inspired zero-noise extrapolation", Physical Review A 110 1, 012404 (2024).
[208] Kento Tsubouchi, Takahiro Sagawa, and Nobuyuki Yoshioka, "Universal Cost Bound of Quantum Error Mitigation Based on Quantum Estimation Theory", Physical Review Letters 131 21, 210601 (2023).
[209] Thomas Schuster, Chao Yin, Xun Gao, and Norman Y. Yao, "A Polynomial-Time Classical Algorithm for Noisy Quantum Circuits", Physical Review X 15 4, 041018 (2025).
[210] M. D. Rahatul Ashakin, Quantum Informatics for Novel Therapeutics 59 (2026) ISBN:978-3-032-19535-7.
[211] Dayue Qin, Yanzhu Chen, and Ying Li, "Error statistics and scalability of quantum error mitigation formulas", npj Quantum Information 9 1, 35 (2023).
[212] Sarmed A Rahman, Randy Lewis, Emanuele Mendicelli, and Sarah Powell, "Self-mitigating Trotter circuits for SU(2) lattice gauge theory on a quantum computer", Physical Review D 106 7, 074502 (2022).
[213] Kaitlin N. Smith, Michael A. Perlin, Pranav Gokhale, Paige Frederick, David Owusu-Antwi, Richard Rines, Victory Omole, and Frederic Chong, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.
[214] Kimchhor Chiv, Leanghok Hour, Sanghyeon Lee, Tara Kit, Tae-Kyung Kim, and Youngsun Han, "Strategies for Noise-Resilient Quantum Approximate Optimization Algorithms: A Review and Classification of Error Mitigation", IEEE Access 13, 216916 (2025).
[215] Daniel Bultrini, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Patrick J. Coles, and Lukasz Cincio, "Unifying and benchmarking state-of-the-art quantum error mitigation techniques", Quantum 7, 1034 (2023).
[216] Yuta Hirasaki, Toshinari Itoko, Naoki Kanazawa, and Eiji Saitoh, "Shift of quantum critical point of discrete time crystal on a noisy quantum simulator", Applied Physics Letters 128 5, 054002 (2026).
[217] Andrey Zhukov and Walter Pogosov, "Quantum error mitigation in the regime of high noise using deep neural network: Trotterized dynamics", Quantum Information Processing 23 3, 80 (2024).
[218] Jessie M. Henderson, Marianna Podzorova, M. Cerezo, John K. Golden, Leonard Gleyzer, Hari S. Viswanathan, and Daniel O’Malley, "Quantum algorithms for geologic fracture networks", Scientific Reports 13 1, 2906 (2023).
[219] Nhung H. Nguyen, Minh C. Tran, Yingyue Zhu, Alaina M. Green, C. Huerta Alderete, Zohreh Davoudi, and Norbert M. Linke, "Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions", PRX Quantum 3 2, 020324 (2022).
[220] Ivan Henao, Jader P. Santos, and Raam Uzdin, "Adaptive quantum error mitigation using pulse-based inverse evolutions", npj Quantum Information 9 1, 120 (2023).
[221] Shaojun Guo, Jinzhao Sun, Haoran Qian, Ming Gong, Yukun Zhang, Fusheng Chen, Yangsen Ye, Yulin Wu, Sirui Cao, Kun Liu, Chen Zha, Chong Ying, Qingling Zhu, He-Liang Huang, Youwei Zhao, Shaowei Li, Shiyu Wang, Jiale Yu, Daojin Fan, Dachao Wu, Hong Su, Hui Deng, Hao Rong, Yuan Li, Kaili Zhang, Tung-Hsun Chung, Futian Liang, Jin Lin, Yu Xu, Lihua Sun, Cheng Guo, Na Li, Yong-Heng Huo, Cheng-Zhi Peng, Chao-Yang Lu, Xiao Yuan, Xiaobo Zhu, and Jian-Wei Pan, "Experimental quantum computational chemistry with optimized unitary coupled cluster ansatz", Nature Physics 20 8, 1240 (2024).
[222] Sergio Hernández López, Danel Arias Álamo, Javier Lázaro González, Javier Ibarra Veganzones, Aitor Morais Miñambres, Iker Pastor López, and Pablo Garcia Bringas, Lecture Notes in Computer Science 15834, 26 (2026) ISBN:978-981-96-7422-0.
[223] Chirag Wadhwa, Laura Lewis, Elham Kashefi, and Mina Doosti, "Agnostic Process Tomography", PRX Quantum 6 4, 040371 (2025).
[224] Quan Fu, Jie Liu, Xin Wang, and Rui Xiong, "Machine Learning the Decoherence Property of Superconducting and Semiconductor Quantum Devices from Graph Connectivity", Entropy 28 1, 89 (2026).
[225] Kondamudi Sivaparvathi and Cheppali Prabhavathi, 2026 4th International Conference on Knowledge Engineering and Communication Systems (ICKECS) 1 (2026) ISBN:979-8-3315-4777-6.
[226] Shi‐Xin Zhang, Zhou‐Quan Wan, Chang‐Yu Hsieh, Hong Yao, and Shengyu Zhang, "Variational Quantum‐Neural Hybrid Error Mitigation", Advanced Quantum Technologies 6 10, 2300147 (2023).
[227] Victor F. dos Santos, Victor P. Brasil, Pedro A. S. Contri, and Jonas Maziero, "Prime Number Identification Demonstrated With Quantum Processors Using a New Rescaling‐Based Noise Mitigation Technique", Advanced Quantum Technologies 9 6, e70342 (2026).
[228] Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson, "The Variational Quantum Eigensolver: A review of methods and best practices", Physics Reports 986, 1 (2022).
[229] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alán Aspuru-Guzik, "Noisy intermediate-scale quantum algorithms", Reviews of Modern Physics 94 1, 015004 (2022).
[230] Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan, "Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation", Journal of the Physical Society of Japan 90 3, 032001 (2021).
[231] Bálint Koczor, "Exponential Error Suppression for Near-Term Quantum Devices", Physical Review X 11 3, 031057 (2021).
[232] Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C. Benjamin, and Ying Li, "Learning-Based Quantum Error Mitigation", PRX Quantum 2 4, 040330 (2021).
[233] William J. Huggins, Sam McArdle, Thomas E. O'Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush, and Jarrod R. McClean, "Virtual Distillation for Quantum Error Mitigation", Physical Review X 11 4, 041036 (2021).
[234] Miroslav Urbanek, Benjamin Nachman, Vincent R. Pascuzzi, Andre He, Christian W. Bauer, and Wibe A. de Jong, "Mitigating Depolarizing Noise on Quantum Computers with Noise-Estimation Circuits", Physical Review Letters 127 27, 270502 (2021).
[235] Nikolay V. Tkachenko, James Sud, Yu Zhang, Sergei Tretiak, Petr M. Anisimov, Andrew T. Arrasmith, Patrick J. Coles, Lukasz Cincio, and Pavel A. Dub, "Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in the Variational Quantum Eigensolver", PRX Quantum 2 2, 020337 (2021).
[236] Ryuji Takagi, "Optimal resource cost for error mitigation", Physical Review Research 3 3, 033178 (2021).
[237] Angus Lowe, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio, "Unified approach to data-driven quantum error mitigation", Physical Review Research 3 3, 033098 (2021).
[238] Joseph Vovrosh, Kiran E. Khosla, Sean Greenaway, Christopher Self, M. S. Kim, and Johannes Knolle, "Simple mitigation of global depolarizing errors in quantum simulations", Physical Review E 104 3, 035309 (2021).
[239] Jinzhao Sun, Xiao Yuan, Takahiro Tsunoda, Vlatko Vedral, Simon C. Benjamin, and Suguru Endo, "Mitigating Realistic Noise in Practical Noisy Intermediate-Scale Quantum Devices", Physical Review Applied 15 3, 034026 (2021).
[240] Alexander Zlokapa and Alexandru Gheorghiu, "A deep learning model for noise prediction on near-term quantum devices", arXiv:2005.10811, (2020).
[241] Alejandro Sopena, Max Hunter Gordon, Germán Sierra, and Esperanza López, "Simulating quench dynamics on a digital quantum computer with data-driven error mitigation", Quantum Science and Technology 6 4, 045003 (2021).
[242] Gokul Subramanian Ravi, Pranav Gokhale, Yi Ding, William M. Kirby, Kaitlin N. Smith, Jonathan M. Baker, Peter J. Love, Henry Hoffmann, Kenneth R. Brown, and Frederic T. Chong, "CAFQA: A classical simulation bootstrap for variational quantum algorithms", arXiv:2202.12924, (2022).
[243] Andrea Mari, Nathan Shammah, and William J. Zeng, "Extending quantum probabilistic error cancellation by noise scaling", Physical Review A 104 5, 052607 (2021).
[244] Youngseok Kim, Christopher J. Wood, Theodore J. Yoder, Seth T. Merkel, Jay M. Gambetta, Kristan Temme, and Abhinav Kandala, "Scalable error mitigation for noisy quantum circuits produces competitive expectation values", arXiv:2108.09197, (2021).
[245] Xinbiao Wang, Yuxuan Du, Yong Luo, and Dacheng Tao, "Towards understanding the power of quantum kernels in the NISQ era", Quantum 5, 531 (2021).
[246] Ashley Montanaro and Stasja Stanisic, "Error mitigation by training with fermionic linear optics", arXiv:2102.02120, (2021).
[247] Piotr Czarnik, Andrew Arrasmith, Lukasz Cincio, and Patrick J. Coles, "Qubit-efficient exponential suppression of errors", arXiv:2102.06056, (2021).
[248] Steven T. Flammia, "Averaged circuit eigenvalue sampling", arXiv:2108.05803, (2021).
[249] Zhenyu Cai, "A Practical Framework for Quantum Error Mitigation", arXiv:2110.05389, (2021).
[250] Hanrui Wang, Yongshan Ding, Jiaqi Gu, Zirui Li, Yujun Lin, David Z. Pan, Frederic T. Chong, and Song Han, "QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits", arXiv:2107.10845, (2021).
[251] Javier Argüello-Luengo, Tao Shi, and Alejandro González-Tudela, "Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices", Physical Review A 103 4, 043318 (2021).
[252] Yongdan Yang, Bing-Nan Lu, and Ying Li, "Accelerated Quantum Monte Carlo with Mitigated Error on Noisy Quantum Computer", PRX Quantum 2 4, 040361 (2021).
[253] Daiqin Su, Robert Israel, Kunal Sharma, Haoyu Qi, Ish Dhand, and Kamil Brádler, "Error mitigation on a near-term quantum photonic device", Quantum 5, 452 (2021).
[254] Michael R. Geller, "Conditionally Rigorous Mitigation of Multiqubit Measurement Errors", Physical Review Letters 127 9, 090502 (2021).
[255] Dayue Qin, Xiaosi Xu, and Ying Li, "An overview of quantum error mitigation formulas", Chinese Physics B 31 9, 090306 (2022).
[256] Keisuke Fujii, Kaoru Mizuta, Hiroshi Ueda, Kosuke Mitarai, Wataru Mizukami, and Yuya O. Nakagawa, "Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers", arXiv:2007.10917, (2020).
[257] Changjun Kim, Kyungdeock Daniel Park, and June-Koo Rhee, "Quantum Error Mitigation With Artificial Neural Network", IEEE Access 8, 188853 (2020).
[258] Kun Wang, Yu-Ao Chen, and Xin Wang, "Mitigating Quantum Errors via Truncated Neumann Series", arXiv:2111.00691, (2021).
[259] Andrii Maksymov, Jason Nguyen, Yunseong Nam, and Igor Markov, "Enhancing quantum computer performance via symmetrization", arXiv:2301.07233, (2023).
[260] Kun Wang, Yu-Ao Chen, and Xin Wang, "Measurement Error Mitigation via Truncated Neumann Series", arXiv:2103.13856, (2021).
[261] Robin Blume-Kohout, Kenneth Rudinger, Erik Nielsen, Timothy Proctor, and Kevin Young, "Wildcard error: Quantifying unmodeled errors in quantum processors", arXiv:2012.12231, (2020).
[262] Rishabh Gupta, Raphael D. Levine, and Sabre Kais, "Convergence of a Reconstructed Density Matrix to a Pure State Using the Maximal Entropy Approach", Journal of Physical Chemistry A 125 34, 7588 (2021).
[263] V. Leyton-Ortega, S. Majumder, and R. C. Pooser, "Quantum error mitigation by hidden inverses protocol in superconducting quantum devices", Quantum Science and Technology 8 1, 014008 (2023).
[264] Laia Domingo, "Classical and quantum reservoir computing: development and applications in machine learning", arXiv:2310.07455, (2023).
[265] Enrico Fontana, Ivan Rungger, Ross Duncan, and Cristina Cîrstoiu, "Spectral analysis for noise diagnostics and filter-based digital error mitigation", arXiv:2206.08811, (2022).
[266] Lukasz Cincio, Kenneth Rudinger, Mohan Sarovar, and Patrick J. Coles, "Machine learning of noise-resilient quantum circuits", arXiv:2007.01210, (2020).
[267] Jinzhao Sun, Xiao Yuan, Takahiro Tsunoda, Vlatko Vedral, Simon C. Bejamin, and Suguru Endo, "Mitigating realistic noise in practical noisy intermediate-scale quantum devices", arXiv:2001.04891, (2020).
[268] Alistair W. R. Smith, Kiran E. Khosla, Chris N. Self, and M. S. Kim, "Qubit Readout Error Mitigation with Bit-flip Averaging", arXiv:2106.05800, (2021).
[269] Xuanqiang Zhao, Benchi Zhao, Zihan Xia, and Xin Wang, "Information recoverability of noisy quantum states", Quantum 7, 978 (2023).
[270] Zhen Wang, Yanzhu Chen, Zixuan Song, Dayue Qin, Hekang Li, Qiujiang Guo, H. Wang, Chao Song, and Ying Li, "Scalable Evaluation of Quantum-Circuit Error Loss Using Clifford Sampling", Physical Review Letters 126 8, 080501 (2021).
[271] Siddharth Dangwal, Gokul Subramanian Ravi, Poulami Das, Kaitlin N. Smith, Jonathan M. Baker, and Frederic T. Chong, "VarSaw: Application-tailored Measurement Error Mitigation for Variational Quantum Algorithms", arXiv:2306.06027, (2023).
[272] Jessie M. Henderson, Marianna Podzorova, M. Cerezo, John K. Golden, Leonard Gleyzer, Hari S. Viswanathan, and Daniel O'Malley, "Quantum Algorithms for Geologic Fracture Networks", arXiv:2210.11685, (2022).
[273] Hrushikesh Patil, Peiyi Li, Ji Liu, and Huiyang Zhou, "Folding-Free ZNE: A Comprehensive Quantum Zero-Noise Extrapolation Approach for Mitigating Depolarizing and Decoherence Noise", arXiv:2305.00622, (2023).
[274] Yusen Wu and Jingbo B. Wang, "Estimating Gibbs partition function with quantum Clifford sampling", Quantum Science and Technology 7 2, 025006 (2022).
[275] Vedika Saravanan and Samah M. Saeed, "Data-Driven Reliability Models of Quantum Circuit: From Traditional ML to Graph Neural Network", IEEE Transactions on Computer Aided Design 42 5, 1477 (2023).
[276] Yifeng Xiong, Soon Xin Ng, and Lajos Hanzo, "Quantum Error Mitigation Relying on Permutation Filtering", arXiv:2107.01458, (2021).
[277] Daniel Bultrini, Max Hunter Gordon, Esperanza López, and Germȧn Sierra, "Simple Mitigation Strategy for a Systematic Gate Error in IBMQ", arXiv:2012.00831, (2020).
[278] Syahri Ramadhani, Junaid Ur Rehman, and Hyundong Shin, "Quantum Error Mitigation for Quantum State Tomography", IEEE Access 9, 107955 (2021).
[279] Yifeng Xiong, Daryus Chandra, Soon Xin Ng, and Lajos Hanzo, "Circuit Symmetry Verification Mitigates Quantum-Domain Impairments", arXiv:2112.13904, (2021).
[280] Dorit Aharonov, Ori Alberton, Itai Arad, Yosi Atia, Eyal Bairey, Matan Ben Dov, Asaf Berkovitch, Zvika Brakerski, Itsik Cohen, Eran Fuchs, Omri Golan, Or Golan, Barak D. Gur, Ilya Gurwich, Avieli Haber, Rotem Haber, Dorri Halbertal, Yaron Itkin, Barak A. Katzir, Oded Kenneth, Shlomi Kotler, Roei Levi, Eyal Leviatan, Yotam Y. Lifshitz, Adi Ludmer, Shlomi Matityahu, Ron Aharon Melcer, Adiel Meyer, Omrie Ovdat, Aviad Panahi, Gil Ron, Ittai Rubinstein, Gili Schul, Tali Shnaider, Maor Shutman, Asif Sinay, Tasneem Watad, Assaf Zubida, and Netanel H. Lindner, "Reliable high-accuracy error mitigation for utility-scale quantum circuits", arXiv:2508.10997, (2025).
[281] Alexander Kunitsa, Nicole Bellonzi, Shangjie Guo, Jérôme F. Gonthier, Corneliu Buda, Clena M. Abuan, and Jhonathan Romero, "Experimental demonstration of Robust Amplitude Estimation on near-term quantum devices for chemistry applications", arXiv:2410.00686, (2024).
[282] Siddharth Dangwal, Suhas Vittal, Lennart Maximillian Seifert, Frederic T. Chong, and Gokul Subramanian Ravi, "Variational Quantum Algorithms in the era of Early Fault Tolerance", arXiv:2503.20963, (2025).
[283] Hrushikesh Pramod Patil, Dror Baron, and Huiyang Zhou, "Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning", arXiv:2504.10801, (2025).
[284] Qingfeng Wang, Liudmila Zhukas, Qiang Miao, Aniket S. Dalvi, Peter J. Love, Christopher Monroe, Frederic T. Chong, and Gokul Subramanian Ravi, "Demonstration of a CAFQA-bootstrapped Variational Quantum Eigensolver on a Trapped-Ion Quantum Computer", arXiv:2408.06482, (2024).
[285] Julien Gacon, "Scalable Quantum Algorithms for Noisy Quantum Computers", arXiv:2403.00940, (2024).
[286] Peiyi Li, Ji Liu, Alvin Gonzales, Zain Hamid Saleem, Huiyang Zhou, and Paul Hovland, "QuTracer: Mitigating Quantum Gate and Measurement Errors by Tracing Subsets of Qubits", arXiv:2404.19712, (2024).
[287] Philip Döbler, Jannik Pflieger, Fengping Jin, Hans De Raedt, Kristel Michielsen, Thomas Lippert, and Manpreet Singh Jattana, "Scalable General Error Mitigation for Quantum Circuits", arXiv:2411.07916, (2024).
[288] Dror Baron, Hrushikesh Pramod Patil, and Huiyang Zhou, "Maximum Likelihood Quantum Error Mitigation for Algorithms with a Single Correct Output", arXiv:2402.11830, (2024).
[289] Yinchen Liu, James R. Seddon, Tamara Kohler, Emilio Onorati, and Toby S. Cubitt, "Robust Lindbladian Estimation for Quantum Dynamics", arXiv:2507.07912, (2025).
[290] Simone Cantori, Andrea Mari, David Vitali, and Sebastiano Pilati, "Deep-learned error mitigation via partially knitted circuits for the variational quantum eigensolver", arXiv:2506.04146, (2025).
[291] Elijah Pelofske and Vincent Russo, "Digital Zero-Noise Extrapolation with Quantum Circuit Unoptimization", arXiv:2503.06341, (2025).
[292] Laurin E. Fischer, "Enabling large-scale digital quantum simulations with superconducting qubits", arXiv:2602.04719, (2026).
[293] Alessandro Cosentino, Changhao Li, Vincent Russo, Bradley A. Chase, Tom Lubinski, Siyuan Niu, Neer Patel, Nathan Shammah, and William J. Zeng, "Metriq: A Collaborative Platform for Benchmarking Quantum Computers", arXiv:2603.08680, (2026).
[294] Pradeep Mantha, Florian J. Kiwit, Nishant Saurabh, Shantenu Jha, and Andre Luckow, "Hybrid Quantum-HPC Middleware Systems for Adaptive Resource, Workload and Task Management", arXiv:2604.03445, (2026).
[295] Zhenyu Chen, Bin Cheng, Minbo Gao, Xiaodie Lin, Ruiqi Zhang, Zhaohui Wei, and Zhengfeng Ji, "Scalable Quantum Error Mitigation with Neighbor-Informed Learning", arXiv:2512.12578, (2025).
[296] Leonardo Placidi, Ifan Williams, Enrico Rinaldi, Daniel Mills, Cristina Cîrstoiu, Vanya Eccles, and Ross Duncan, "Deep Learning Approaches to Quantum Error Mitigation", arXiv:2601.14226, (2026).
[297] Qingxin Yang and Stefano Markidis, "When Noisy Quantum Order Finding Remains Recoverable for Shor's Algorithm", arXiv:2605.16074, (2026).
[298] Steven Szachara, Sheeraja Rajakrishnan, Dylan Jay Van Allen, Jason Pollack, Travis Desell, and Daniel Krutz, "GSC-QEMit: A Telemetry-Driven Hierarchical Forecast-and-Bandit Framework for Adaptive Quantum Error Mitigation", arXiv:2604.24551, (2026).
[299] Sahil Al Farib, Sheikh Redwanul Islam, and Azizur Rahman Anik, "Few-Shot Cross-Device Transfer for Quantum Noise Modeling on Real Hardware", arXiv:2604.24397, (2026).
[300] Fadhil Fatih Shiddiq, Darell Timothy Tarigan, Hadyan Luthfan Prihadi, Jusak S. Kosasih, Yanoar P. Sarwono, Leong-Chuan Kwek, and Freddy Permana Zen, "Pauli Weight Hamiltonian Term Selection for Optimized Machine Learning Based Quantum Error Mitigation", arXiv:2606.31195, (2026).
[301] Vicenzo Scavino Alfaro, "Certified Finite-Shot Operating Windows for Virtual Distillation and Symmetry Verification", arXiv:2606.15464, (2026).
[302] Vicenzo Scavino, "Finite-shot operating windows for probabilistic error cancellation and Clifford data regression", arXiv:2606.21686, (2026).
[303] Ning Ma, Jun Dai, and Heng Li, "Backend-Aware Graph Learning for Denoising Outcome Distributions in Quantum Program Testing", arXiv:2607.23211, (2026).
[304] Dominik Köster and Wolfgang Mauerer, "Claim against Measurement: Statistical Artefacts in Quantum Error Mitigation Benchmarks", arXiv:2605.29872, (2026).
[305] Vicenzo Scavino, "Decision Kernels for Quantum Error Mitigation: Why Accuracy Gains Need Not Improve Downstream Decisions", arXiv:2607.02888, (2026).
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